Numerical Analysis of a High-Order Scheme for Nonlinear Fractional Differential Equations with Uniform Accuracy

2020/02/22 by Cao, Junying, Cai, Zhenning
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2002.09733

Abstract

We introduce a high-order numerical scheme for fractional ordinary differential equations with the Caputo derivative. The method is developed by dividing the domain into a number of subintervals, and applying the quadratic interpolation on each subinterval. The method is shown to be unconditionally stable, and for general nonlinear equations, the uniform sharp numerical order 3-ν can be rigorously proven for sufficiently smooth solutions at all time steps. The proof provides a general guide for proving the sharp order for higher-order schemes in the nonlinear case. Some numerical examples are given to validate our theoretical results.

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